Solutions For Advection-dominated Accretion Flows Research Articles

Heating or Cooling: Study of Advective Heat Transport in the Inflow and the Outflow of Optically Thin Advection-dominated Accretion Flows

Advection is believed to be the dominant cooling mechanism in optically thin advection-dominated accretion flows (ADAFs). When outflow is considered, however, the first impression is that advection should be of opposite sign in the inflow and the outflow, due to the opposite direction of radial motion. Then how is the energy balance achieved simultaneously? We investigate the problem in this paper, analyzing the profiles of different components of advection with self-similar solutions of ADAFs in spherical coordinates (r θ ϕ). We find that for n < 3γ/2 − 1, where n is the density index in ρ ∝ r −n and γ is the heat capacity ratio, the radial advection is a heating mechanism in the inflow and a cooling mechanism in the outflow. It becomes 0 for n = 3γ/2 − 1, and turns to a cooling mechanism in the inflow and a heating mechanism in the outflow for n > 3γ/2 − 1. The energy conservation is only achieved when the latitudinal (θ direction) advection is considered, which takes an appropriate value to maintain energy balance, so that the overall effect of advection, no matter the parameter choices, is always a cooling mechanism that cancels out the viscous heating everywhere. For the extreme case of n = 3/2, latitudinal motion stops, viscous heating is balanced solely by radial advection, and no outflow is developed.

Fourier Analysis of Advection-dominated Accretion Flows

Abstract We implement a new semi-analytical approach to investigate radially self-similar solutions for the steady-state advection-dominated accretion flows (ADAFs). We employ the usual α-prescription for the viscosity, and all components of the energy–momentum tensor are considered. In this case, in the spherical coordinate, the problem reduces to a set of eighth-order, nonlinear differential equations with respect to the latitudinal angle θ. Using the Fourier expansions for all the flow quantities, we convert the governing differential equations to a large set of nonlinear algebraic equations for the Fourier coefficients. We solve the algebraic equations via the Newton–Raphson method, and investigate the ADAF properties over a wide range of model parameters. We also show that the implemented series are truly convergent. The main advantage of our numerical method is that it does not suffer from the usual technical restrictions that may arise for solving ADAF differential equations near the polar axis. In order to check the reliability of our approach, we recover some widely studied solutions. Further, we introduce a new varying α viscosity model. New outflow and inflow solutions for ADAFs are also presented, using Fourier expansion series.

Self-similar solutions of viscous and resistive ADAFs with thermal conduction

We have studied the effects of thermal conduction on the structure of viscous and resistive advection-dominated accretion flows (ADAFs). The importance of thermal conduction on hot accretion flow is confirmed by observations of hot gas that surrounds Sgr A$^*$ and a few other nearby galactic nuclei. In this research, thermal conduction is studied by a saturated form of it, as is appropriated for weakly-collisional systems. It is assumed the viscosity and the magnetic diffusivity are due to turbulence and dissipation in the flow. The viscosity also is due to angular momentum transport. Here, the magnetic diffusivity and the kinematic viscosity are not constant and vary by position and $\alpha$-prescription is used for them. The govern equations on system have been solved by the steady self-similar method. The solutions show the radial velocity is highly subsonic and the rotational velocity behaves sub-Keplerian. The rotational velocity for a specific value of the thermal conduction coefficient becomes zero. This amount of conductivity strongly depends on magnetic pressure fraction, magnetic Prandtl number, and viscosity parameter. Comparison of energy transport by thermal conduction with the other energy mechanisms implies that thermal conduction can be a significant energy mechanism in resistive and magnetized ADAFs. This property is confirmed by non-ideal magnetohydrodynamics (MHD) simulations.

Bondi flow from a slowly rotating hot atmosphere

A supermassive black hole in the nucleus of an elliptical galaxy at the centre of a cool-core group or cluster of galaxies is immersed in hot gas. Bondi accretion should occur at a rate determined by the properties of the gas at the Bondi radius and the mass of the black hole. X-ray observations of massive nearby elliptical galaxies, including M87 in the Virgo cluster, indicate a Bondi accretion rate Mdot which roughly matches the total kinetic power of the jets, suggesting that there is a tight coupling between the jet power and the mass accretion rate. While the Bondi model considers non-rotating gas, it is likely that the external gas has some angular momentum, which previous studies have shown could decrease the accretion rate drastically. We investigate here the possibility that viscosity acts at all radii to transport angular momentum outward so that the accretion inflow proceeds rapidly and steadily. The situation corresponds to a giant Advection Dominated Accretion Flow (ADAF) which extends from beyond the Bondi radius down to the black hole. We find solutions of the ADAF equations in which the gas accretes at just a factor of a few less than Mdot. These solutions assume that the atmosphere beyond the Bondi radius rotates with a sub-Keplerian velocity and that the viscosity parameter is large, alpha~0.1. The infall time of the ADAF solutions is no more than a few times the free-fall time. Thus the accretion rate at the black hole is closely coupled to the surrounding gas, enabling tight feedback to occur. We show that jet powers of a few per cent of Mdot c^2 are expected if either a fraction of the accretion power is channeled into the jet or the black hole spin energy is tapped by a strong magnetic field pressed against the black hole by the pressure of the accretion flow.(Truncated)

Self-similar solution of hot accretion flows with ordered magnetic field and outflow

Observations and numerical magnetohydrodynamic (MHD) simulations indicate the existence of outflows and ordered large-scale magnetic fields in the inner region of hot accretion flows. In this paper we present the self-similar solutions for advection-dominated accretion flows (ADAFs) with outflows and ordered magnetic fields. Stimulated by numerical simulations, we assume that the magnetic field has a strong toroidal component and a vertical component in addition to a stochastic component. We obtain the self-similar solutions to the equations describing the magnetized ADAFs, taking into account the dynamical effects of the outflow. We compare the results with the canonical ADAFs and find that the dynamical properties of ADAFs such as radial velocity, angular velocity and temperature can be significantly changed in the presence of ordered magnetic fields and outflows. The stronger the magnetic field is, the lower the temperature of the accretion flow will be, and the faster the flow rotates. The relevance to observations is briefly discussed.

Jet Power Extracted from ADAF and the Applications to X‐Ray Binaries and the Radio Galaxy FR Dichotomy

We calculate the jet power of the classical Blandford-Znajek (BZ) model and hybrid model developed by Meier based on the global solutions of advection-dominated accretion flows (ADAFs) surrounding Kerr black holes. We find that the jet power of the hybrid model is larger than that of the pure BZ model. The jet power will dominate over the accretion power, and the objects will enter into jet-power-dominated advective systems,'' when the accretion rate is less than a critical value m(c) = M-c/M-Edd, where 3 x 10(-4) less than or similar to m(c) less than or similar to 5 x 10(-3) is a function of black hole spin parameter. The accretion power will be dominant when m greater than or similar to m(c), and the objects will enter into accretion-power-dominated advective systems.'' This is roughly consistent with that constrained from the low/hard-state black hole X-ray binaries (e. g., Fender et al.). We calculate the maximal jet power as a function of black hole mass with the hybrid jet formation model, and find it can roughly reproduce the dividing line of the Ledlow-Owen relation for FR I/FR II dichotomy in jet the power-black hole (BH) mass plane (Q(jet)-M-BH) if the dimensionless accretion rate m similar to 0.01 and BH spin parameter j similar to 0.9-0.99 are adopted. This accretion rate m similar to 0.01 is consistent with that of the critical accretion rate for the accretion mode transition of a standard disk to an ADAF constrained from the state transition of X-ray binaries. Our results imply that most FR I galaxies may be in the ADAF accretion mode similar to the low/hard-state XRBs.

Hot accretion with outflow and thermal conduction

We present self-similar solutions for advection-dominated accretion flows with thermal conduction in the presence of outflows. Possible effects of outflows on the accretion flow are parametrized and a saturated form of thermal conduction, as is appropriate for the weakly-collisional regime of interest, is included in our model. While the cooling effect of outflows is noticeable, thermal conduction provides an extra heating source. In comparison to accretion flows without winds, we show that the disc rotates faster and becomes cooler because of the angular momentum and energy flux which are taking away by the winds. But thermal conduction opposes the effects of winds and not only decreases the rotational velocity, but increases the temperature. However, reduction of the surface density and the enhanced accretion velocity are amplified by both of the winds and the thermal conduction. We find that for stronger outflows, a higher level of saturated thermal conduction is needed to significantly modify the physical profiles of the accretion flow.

Advection-dominated accretion flows with causal viscosity

We present the basic equations and sample solutions for the steady-state global transonic solutions of the advection-dominated accretion flows (ADAFs) with a causal viscosity prescription. The procedures for the stable numerical calculations and all explicit formula for obtaining the solutions of ADAFs are also presented. We solve the transonic solutions of ADAFs by using the explicit numerical integrations, as in the Runge-Kutta method. In this calculation method, we first solve the physical values at the sonic radius where L'Hopital's rule is used. Then, we numerically solve the coupled differential equations of the radial velocity, the angular momentum, and the sound speed from the sonic radius in the inward and outward directions. By the calculation procedures presented in this paper, we can cover all parameter spaces of the transonic solutions of ADAFs. Sample transonic solutions for ADAF-thick disk and ADAF-thin disk are presented. The explicit formula for the analytical expansion around the singular points, the sonic and the viscous points, are presented. If we set the diffusion timescale to null, the formalism in this study becomes the formalism of the acausal viscosity that is usually used in past studies for calculating of the ADAF structure.

Origin of Radio Emission from Nearby Low‐Luminosity Active Galactic Nuclei

We use the observational data in radio, optical, and X-ray wave bands for a sample of active galactic nuclei (AGNs) with measured black hole masses to explore the origin of radio emission from nearby low-luminosity active galactic nuclei (LLAGNs). The maximal luminosity of an advection-dominated accretion flow (ADAF) can be calculated for a given black hole mass, as there is a critical accretion rate above which the ADAF is no longer present. We find that the radio luminosities are higher than the maximal luminosities expected from the ADAF model for most sources in this sample. This implies that the radio emission is predominantly from the jets in these sources. The radio emission from a small fraction of the sources (15/60; referred to as radio-weak sources) in this sample can be explained by the ADAF model. However, comparing the observed multiband emission data with the spectra calculated for the ADAF or adiabatic inflow-outflow solution (ADIOS) cases, we find that neither ADAF nor ADIOS models can reproduce the observed multiband emission simultaneously, with reasonable magnetic field strengths, for these radio-weak sources. A variety of other possibilities are discussed, and we suggest that the radio emission is probably dominated by jet emission even in these radio-weak LLAGNs.

Global Structures of Optically Thin Black Hole Accretion Flows Obtained from Direct Magnetohydrodynamic Simulations

We studied the global structures of radiatively inefficient black hole accretion flows by three-dimensional magnetohydrodynamic simulations. The initial state is a constant angular-momentum torus threaded by weak toroidal magnetic fields. The torus is assumed to be embedded in a low-density, spherical, isothermal halo. We found that in the innermost region ($\varpi &amp;lt; 15 \,r_g$: $r_g$ is the Schwarzschild radius) of optically thin hot disks formed by accretion from the torus, the radial structure can be described by a one-dimensional steady transonic ADAF (Advection Dominated Accretion Flow) solution that takes into account the radial dependence of $\alpha$. Numerical results indicate that the magnetic flux emerging from the disk creates a magnetically active layer in which magnetic reconnection generates outflows along magnetic field lines. We also studied the dependence of the disk structure on the external pressure of the initial torus. The saturation level of magnetic field amplification is higher for a model with a larger external pressure. Thus, external pressure enhances the magnetic activity of the disk. When the external pressure is 5–20% of the maximum pressure of the torus, the kinetic and Poynting energy flux of the outflow is about 1% of the energy flux advected to the black hole through accretion.

A model for quasi-spherical magnetized accretion flow

A model for axisymmetric magnetized accretion flow is proposed. The dominant mechanism of energy dissipation is assumed to be the magnetic diffusivity due to turbulence in the accretion flow. In analogy to the advection-dominated accretion flow (ADAF) solutions, a constant fraction of the resistively dissipated energy is stored in the accreting gas and the rest is radi- ated. We first introduce the general self-similar solutions which describe a resistive and nonrotating flow with purely poloidal magnetic field. The radial dependence of physical quantities is identical to that in viscous ADAF solutions. Although the main focus of this study is on nonrotating magnetized accretion flow, for rotating flow with both poloidal and toroidal components of magnetic field we find a radial scaling of solutions similar to the nonrotating case. We show that the accretion and the rotation velocities are both below the Keplerian rate, irrespective of the amount of cooling. We show that the set of equations is reduced to one second order differential equation for a nonrotating flow. The geometrical shape of the disk changes depending on the fraction of the resistively dissipated energy which is stored in the accreting gas. However, there is a hot low-density gas above the disk in almost all cases. The net accretion rate is calculated for a set of illustrative parameters.

The Shakura-Sunyaev Disk Can Smoothly Match an Advection-dominated Accretion Flow

We use the standard Runge-Kutta method to solve a set of basic equations describing black hole accretion flows composed of two-temperature plasma. We do not invoke any extra energy transport mechanism, such as thermal conduction, and we do not specify any ad hoc outer boundary condition for the advection-dominated accretion flow (ADAF) solution. We find that in the case of high viscosity and nonzero radiative cooling, the ADAF solution can have an asymptotic approach to the Shakura-Sunyaev disk (SSD) solution and that the SSD-ADAF transition radius is close to the central black hole. Our results further prove the mechanism of thermal instability-triggered SSD-ADAF transition suggested previously by Takeuchi & Mineshige and Gu & Lu.

Optically-thick accretion discs with advection

The structures of optically-thick accretion discs with radial advection have been investigated by the iteration and integration algorithms. The advective cooling term changes mostly the inner part of disc solution and even results in an optically-thick advection-dominated accretion flow (ADAF). Three distinct branches - the outer Shakura-Sunyaev disc (SSD), the inner ADAF and the middle transition layer - are found for a super-Eddington disc. The SSD-ADAF transition radius can be estimated as 18(/E)RG where RG is the Schwarzschild radius, is the mass accretion rate and E is the Eddington accretion rate. SSD solutions calculated with the iteration and integration methods are identical, while ADAF solutions obtained by these two methods differ greatly. Detailed algorithms and their differences have been analysed. The iteration algorithm is not self-consistent, since it implies that the dimensionless advection factor ξ is invariant, but in the inner ADAF region the variation of ξ is not negligible. The integration algorithm is always effective for the whole region of an optically-thick disc if the accretion rate is no smaller than 10-4E. For optically-thin discs, the validity of these two algorithms is different. We suggest that the integration method be employed to calculate the global solution of a disc model without assuming ξ to be a constant. We also discuss its application to the emergent continuum spectrum in order to explain observational facts.

Global solutions of advection-dominated accretion flows with two critical points

This paper presents global solutions of advection-dominated accretion flows (ADAFs) around black holes. The global solution passes through two critical points, the sonic point R s and viscous point R v and is thus naturally divided by these points into three radial zones: the subsonic, subviscous outer zone ( R > R v ), the subsonic, superviscous middle zone ( R s < R < R v ), and the supersonic, superviscous inner zone ( R < R s ). We have obtained a complete picture by means of the R s — j parameter space which sums up the situation of ADAF solution at a glance. We find three classes of global solutions: the ADAF-thin disk solution, the ADAF-thick disk solution and the α — X type adiabatic shock-included solution. We also present the unique correspondences among R s , R v and R out of the ADAF-thin disk solutions, where R out is the outer boundary of ADAF. The adiabatic shock in the accretion flow connects the supersonic and superviscous zone of an X-type solution to the subsonic and superviscous zone of an α-type soultion. Because the shock occurs between two superviscous zones, it can exist for flows with either a low or a high viscosity.

Self‐similar Accretion Flows with Convection

We consider height-integrated equations of an advection-dominated accretion flow (ADAF), assuming that there is no mass outflow. We include convection through a mixing length formalism. We seek self-similar solutions in which the rotational velocity and sound speed scale as R^{-1/2}, where R is the radius, and consider two limiting prescriptions for the transport of angular momentum by convection. In one limit, the transport occurs down the angular velocity gradient, so convection moves angular momentum outward. In the other, the transport is down the specific angular momentum gradient, so convection moves angular momentum inward. We also consider general prescriptions which lie in between the two limits. When convection moves angular momentum outward, we recover the usual self-similar solution for ADAFs in which the mass density scales as rho ~ R^{-3/2}. When convection moves angular momentum inward, the result depends on the viscosity coefficient alpha. If alpha>alpha_{crit1} ~ 0.05, we once again find the standard ADAF solution. For alpha<alpha_{crit}, however, we find a non-accreting solution in which rho ~ R^{-1/2}. We refer to this as a solution or a convection-dominated accretion flow. Two-dimensional numerical simulations of ADAFs with values of alpha<0.03 have been reported by several authors. The simulated ADAFs exhibit convection. By virtue of their axisymmetry, convection in these simulations moves angular momentum inward, as we confirm by computing the Reynolds stress. The simulations give rho ~ R^{-1/2}, in good agreement with the convective envelope solution. The R^{-1/2} density profile is not a consequence of mass outflow.

Advection‐dominated Accretion with Infall and Outflows

We present self-similar solutions for advection-dominated accretion flows with radial viscous force in the presence of outflows from the accretion flow or infall. The axisymmetric flow is treated in variables integrated over polar sections and the effects of infall and outflows on the accretion flow are parametrized for possible configurations compatible with the self-similar solution. We investigate the resulting accretion flows for three different viscosity laws and derive upper limits on the viscosity parameter α. In addition, we find a natural connection to nonrotating and spherical accretion with turbulent viscosity, which is assumed to persist even without differential rotation. Positive Bernoulli numbers for advection-dominated accretion allow a fraction of the gas to be expelled in an outflow, and the upper limit on the viscosity predicts that outflows are inevitable for equations of state close to an ideal gas.

The role of advection in the accreting corona model for active galactic nuclei and Galactic black holes

ABSTRA C T We consider the role of advection in a two-temperature accreting corona with an underlying optically thick disc. The properties of coronal solutions depend significantly on the description of advection. Local parametrization of advection by a constant coefficient d replacing the radial derivatives leads to complex solution topology, similar to some extent to other advection-dominated accretion flow solutions. One radiatively cooled branch exists for low accretion rates. For higher accretion rates two solutions exist over a broad range of radii: one is radiatively cooled and the other one is advection-dominated. With further increase of accretion rate, the radial extensions of the two solutions shrink and no solutions are found above a certain critical value. However, these trends change if the local parametrization of advection is replaced by proper radial derivatives computed iteratively from the model. Only one, radiatively cooled solution remains, and it exists even for high accretion rates. The advection-dominated branch disappears during the iteration process, which means that a self-consistently described advection-dominated flow cannot exist in the presence of an underlying cold disc.

Thermal Properties of Two‐dimensional Advection‐dominated Accretion Flow

We study the thermal structure of the widely adopted two-dimensional advection-dominated accretion flow (ADAF) of Narayan & Yi. The critical radius for a given mass accretion rate, outside of which the optically thin hot solutions do not exist in the equatorial plane, agrees with those of one-dimensional studies. However, we find that, even within the critical radius, there always exists a conical region of the flow, around the pole, which cannot maintain the assumed high electron temperature, regardless of the mass accretion rate, in the absence of radiative heating. This could lead to a torus-like advection inflow shape since, in general, the ions too will cool down. We also find that Compton preheating is generally important and, if the radiative efficiency, defined as the luminosity output divided by the mass accretion rate times the velocity of light squared, is above ~4 × 10-3, the polar region of the flow is preheated above the virial temperature by Compton heating, which may result in time-dependent behavior or outflow while accretion continues in the equatorial plane. Thus, under most relevant circumstances, ADAF solutions may be expected to be accompanied by polar outflow winds. While preheating instabilities exist in ADAF, as for spherical flows, the former are to some extent protected by their characteristically higher densities and higher cooling rates, which reduce their susceptibility to Compton driven overheating.